Impact of the Euro 2020 championship on the spread of COVID-19 (preprint)

Large-scale events like the UEFA Euro~2020 football (soccer) championship offer a unique opportunity to quantify the impact of gatherings on the spread of COVID-19, as the number and dates of matches played by participating countries resembles a randomized study. Using Bayesian modeling and the gender imbalance in COVID-19 data, we attribute 840,000 (95% CI: [0.39M, 1.26M]) COVID-19 cases across 12 countries to the championship. The impact depends non-linearly on the initial incidence, the reproduction number $R$, and the number of matches played. The strongest effects are seen in Scotland and England, where as much as 10,000 primary cases per million inhabitants occur from championship-related gatherings. The average match-induced increase in $R$ was 0.46 [0.18, 0.75] on match days, but important matches caused an increase as large as +3. Altogether, our results provide quantitative insights that help judge and mitigate the impact of large-scale events on pandemic spread.

Evaluating vaccine allocation strategies using simulation-assisted causal modelling (preprint)

Early on during a pandemic, vaccine availability is limited, requiring prioritisation of different population groups. Evaluating vaccine allocation is therefore a crucial element of pandemics response. In the present work, we develop a model to retrospectively evaluate age-dependent counterfactual vaccine allocation strategies against the COVID-19 pandemic. To estimate the effect of allocation on the expected severe-case incidence, we employ a simulation-assisted causal modelling approach which combines a compartmental infection-dynamics simulation, a coarse-grained, data-driven causal model and literature estimates for immunity waning. We compare Israel's implemented vaccine allocation strategy in 2021 to counterfactual strategies such as no prioritisation, prioritisation of younger age groups or a strict risk-ranked approach; we find that Israel's implemented strategy was indeed highly effective. We also study the marginal impact of increasing vaccine uptake for a given age group and find that increasing vaccinations in the elderly is most effective at preventing severe cases, whereas additional vaccinations for middle-aged groups reduce infections most effectively. Due to its modular structure, our model can easily be adapted to study future pandemics. We demonstrate this flexibility by investigating vaccine allocation strategies for a pandemic with characteristics of the Spanish Flu. Our approach thus helps evaluate vaccination strategies under the complex interplay of core epidemic factors, including age-dependent risk profiles, immunity waning, vaccine availability and spreading rates.

Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations (preprint)

Background: Short-term forecasts of infectious disease burden can contribute to situational awareness and aid capacity planning. Based on best practice in other fields and recent insights in infectious disease epidemiology, one can maximise the predictive performance of such forecasts if multiple models are combined into an ensemble. Here we report on the performance of ensembles in predicting COVID-19 cases and deaths across Europe between 08 March 2021 and 07 March 2022. Methods: We used open-source tools to develop a public European COVID-19 Forecast Hub. We invited groups globally to contribute weekly forecasts for COVID-19 cases and deaths reported from a standardised source over the next one to four weeks. Teams submitted forecasts from March 2021 using standardised quantiles of the predictive distribution. Each week we created an ensemble forecast, where each predictive quantile was calculated as the equally-weighted average (initially the mean and then from 26th July the median) of all individual models predictive quantiles. We measured the performance of each model using the relative Weighted Interval Score (WIS), comparing models forecast accuracy relative to all other models. We retrospectively explored alternative methods for ensemble forecasts, including weighted averages based on models past predictive performance. Results: Over 52 weeks we collected and combined up to 28 forecast models for 32 countries. We found a weekly ensemble had a consistently strong performance across countries over time. Across all horizons and locations, the ensemble performed better on relative WIS than 84% of participating models forecasts of incident cases (with a total N=862), and 92% of participating models forecasts of deaths (N=746). Across a one to four week time horizon, ensemble performance declined with longer forecast periods when forecasting cases, but remained stable over four weeks for incident death forecasts. In every forecast across 32 countries, the ensemble outperformed most contributing models when forecasting either cases or deaths, frequently outperforming all of its individual component models. Among several choices of ensemble methods we found that the most influential and best choice was to use a median average of models instead of using the mean, regardless of methods of weighting component forecast models. Conclusions: Our results support the use of combining forecasts from individual models into an ensemble in order to improve predictive performance across epidemiological targets and populations during infectious disease epidemics. Our findings further suggest that median ensemble methods yield better predictive performance more than ones based on means. Our findings also highlight that forecast consumers should place more weight on incident death forecasts than incident case forecasts at forecast horizons greater than two weeks.

Interplay between risk perception, behaviour, and COVID-19 spread (preprint)

Pharmaceutical and non-pharmaceutical interventions (NPIs) have been crucial for controlling COVID-19. They are complemented by voluntary health-protective behaviour, building a complex interplay between risk perception, behaviour, and disease spread. We studied how voluntary health-protective behaviour and vaccination willingness impact the long-term dynamics. We analysed how different levels of mandatory NPIs determine how individuals use their leeway for voluntary actions. If mandatory NPIs are too weak, COVID-19 incidence will surge, implying high morbidity and mortality before individuals react; if they are too strong, one expects a rebound wave once restrictions are lifted, challenging the transition to endemicity. Conversely, moderate mandatory NPIs give individuals time and room to adapt their level of caution, mitigating disease spread effectively. When complemented with high vaccination rates, this also offers a robust way to limit the impacts of the Omicron variant of concern. Altogether, our work highlights the importance of appropriate mandatory NPIs to maximise the impact of individual voluntary actions in pandemic control.

The winter dilemma (preprint)

As summer in the northern hemisphere comes to an end, changes in daylight, temperature, and weather -- and people's reaction to them -- will be the drivers of a disadvantageous seasonality of SARS-CoV-2. With the seasonal odds against us, stabilization of new COVID-19 cases and hospitalizations requires high immunity levels in the population or sufficient non-pharmaceutical interventions (NPIs). However, compliance with mandatory NPIs, vaccine uptake, and individual protective measures depend on individual opinions and decisions. This in turn depends on the individuals' communication network, as well as access to and personal consumption of information, e.g., about vaccine safety or current infection levels. Therefore, understanding how individual protection-seeking behavior affects disease spread is crucial to prepare for the upcoming winter and future challenges.

Mutational signatures and transmissibility of SARS-CoV-2 Gamma and Lambda variants (preprint)

The emergence of SARS-CoV-2 variants of concern endangers the long-term control of COVID-19, especially in countries with limited genomic surveillance. In this work, we explored genomic drivers of contagion in Chile. We sequenced 3443 SARS-CoV-2 genomes collected between January and July 2021, where the Gamma (P.1), Lambda (C.37), Alpha (B.1.1.7), B.1.1.348, and B.1.1 lineages were predominant. Using a Bayesian model tailored for limited genomic surveillance, we found that Lambda and Gamma variants' reproduction numbers were about 5% and 16% larger than Alpha's, respectively. We observed an overabundance of mutations in the Spike gene, strongly correlated with the variant's transmissibility. Furthermore, the variants' mutational signatures featured a breakpoint concurrent with the beginning of vaccination (mostly CoronaVac, an inactivated virus vaccine), indicating an additional putative selective pressure. Thus, our work provides a reliable method for quantifying novel variants' transmissibility under subsampling (as newly-reported Delta, B.1.617.2) and highlights the importance of continuous genomic surveillance.

Relaxing restrictions at the pace of vaccination increases freedom and guards against further COVID-19 waves (preprint)

Mass vaccination offers a promising exit strategy for the COVID-19 pandemic. However, as vaccination progresses, demands to lift restrictions increase, despite most of the population remaining susceptible. Using our age-stratified SEIRD-ICU compartmental model and curated epidemiological and vaccination data, we quantified the rate (relative to vaccination progress) at which countries can lift non-pharmaceutical interventions without overwhelming their healthcare systems. We analyzed scenarios ranging from immediately lifting restrictions (accepting high mortality and morbidity) to reducing case numbers to a level where test-trace-and-isolate (TTI) programs efficiently compensate for local spreading events. In general, the age-dependent vaccination roll-out implies a transient decrease of more than ten years in the average age of ICU patients and deceased. The pace of vaccination determines the speed of lifting restrictions; Taking the European Union (EU) as an example case, all considered scenarios allow for steadily increasing contacts starting in May 2021 and relaxing most restrictions by autumn 2021. Throughout summer 2021, only mild contact restrictions will remain necessary. However, only high vaccine uptake can prevent further severe waves. Across EU countries, seroprevalence impacts the long-term success of vaccination campaigns more strongly than age demographics. In addition, we highlight the need for preventive measures to reduce contagion in school settings throughout the year 2021, where children might be drivers of contagion because of them remaining susceptible...

Low case numbers enable long-term stable pandemic control without lockdowns (preprint)

The traditional long-term solutions for epidemic control involve eradication or population immunity. Here, we analytically derive the existence of a third viable solution: a stable equilibrium at low case numbers, where test-trace-and-isolate policies partially compensate for local spreading events, and only moderate restrictions remain necessary. In this equilibrium, daily cases stabilize around ten new infections per million people or less. However, stability is endangered if restrictions are relaxed or case numbers grow too high. The latter destabilization marks a tipping point beyond which the spread self-accelerates. We show that a lockdown can reestablish control and that recurring lockdowns are not necessary given sustained, moderate contact reduction. We illustrate how this strategy profits from vaccination and helps mitigate variants of concern. This strategy reduces cumulative cases (and fatalities) 4x more than strategies that only avoid hospital collapse. In the long term, immunization, large-scale testing, and international coordination will further facilitate control.

Towards a long-term control of COVID-19 at low case numbers (preprint)

The traditional long-term solutions for epidemic control involve eradication or herd immunity. Neither of them will be attained within a few months for the COVID-19 pandemic. Here, we analytically derive the existence of a third, viable solution: a stable equilibrium at low case numbers, where test-trace-and-isolate policies partially compensate for local spreading events, and only moderate contact restrictions remain necessary. Across wide parameter ranges of our complementary compartmental model, the equilibrium is reached at or below 10 daily new cases per million people. Such low levels had been maintained over months in most European countries. However, this equilibrium is endangered (i) if contact restrictions are relaxed, or (ii) if case numbers grow too high. The latter destabilisation marks a novel tipping point beyond which the spread self-accelerates because test-trace-and-isolate capacities are overwhelmed. To reestablish control quickly, a lockdown is required. We show that a lockdown is either effective within a few weeks, or tends to fail its aim. If effective, recurring lockdowns are not necessary -- contrary to the oscillating dynamics previously presented in the context of circuit breakers, and contrary to a regime with high case numbers -- if moderate contact reductions are maintained. Hence, at low case numbers, the control is easier, and more freedom can be granted. We demonstrate that this strategy reduces case numbers and fatalities by a factor of 5 compared to a strategy focused only on avoiding major congestion of hospitals. Furthermore, our solution minimises lockdown duration, and hence economic impact. In the long term, control will successively become easier due to immunity through vaccination or large scale testing programmes. International coordination would facilitate even more the implementation of this solution.

The foreshadow of a second wave: An analysis of current COVID-19 fatalities in Germany (preprint)

A second wave of SARS-CoV-2 is unfolding in dozens of countries. However, this second wave manifests itself strongly in new reported cases, but less in death counts compared to the first wave. Over the past three months in Germany, the reported cases increased by a factor five or more, whereas the death counts hardly grew. This discrepancy fueled speculations that the rise of reported cases would not reflect a second wave but only wider testing. We find that this apparent discrepancy can be explained to a large extent by the age structure of the infected, and predict a pronounced increase of death counts in the near future, as the spread once again expands into older age groups. To re-establish control, and to avoid the tipping point when TTI capacity is exceeded, case numbers have to be lowered. Otherwise the control of the spread and the protection of vulnerable people will require more restrictive measures latest when the hospital capacity is reached.

Model-based and model-free characterization of epidemic outbreaks (preprint)

Here we provide detailed background information for our work on Bayesian inference of change-points in the spread of SARS-CoV-2 and the effectiveness of non-pharmaceutical interventions (Dehning et al., Science, 2020). We outline the general background of Bayesian inference and of SIR-like models. We explain the assumptions that underlie model-based estimates of the reproduction number and compare them to the assumptions that underlie model-free estimates, such as used in the Robert-Koch Institute situation reports. We highlight effects that originate from the two estimation approaches, and how they may cause differences in the inferred reproduction number. Furthermore, we explore the challenges that originate from data availability - such as publication delays and inconsistent testing - and explain their impact on the time-course of inferred case numbers. Along with alternative data sources, this allowed us to cross-check and verify our previous results.

Inferring COVID-19 spreading rates and potential change points for case number forecasts (preprint)

As COVID-19 is rapidly spreading across the globe, short-term modeling forecasts provide time-critical information for decisions on containment and mitigation strategies. A main challenge for short-term forecasts is the assessment of key epidemiological parameters and how they change when first interventions show an effect. By combining an established epidemiological model with Bayesian inference, we analyze the time dependence of the effective growth rate of new infections. Focusing on the COVID-19 spread in Germany, we detect change points in the effective growth rate that correlate well with the times of publicly announced interventions. Thereby, we can quantify the effect of interventions, and we can incorporate the corresponding change points into forecasts of future scenarios and case numbers. Our code is freely available and can be readily adapted to any country or region.

Inferring change points in the COVID-19 spreading reveals the effectiveness of interventions (preprint)

As COVID-19 is rapidly spreading across the globe, short-term modeling forecasts provide time-critical information for decisions on containment and mitigation strategies. A main challenge for short-term forecasts is the assessment of key epidemiological parameters and how they change when first interventions show an effect. By combining an established epidemiological model with Bayesian inference, we analyze the time dependence of the effective growth rate of new infections. Focusing on the COVID-19 spread in Germany, we detect change points in the effective growth rate that correlate well with the times of publicly announced interventions. Thereby, we can quantify the effect of interventions, and we can incorporate the corresponding change points into forecasts of future scenarios and case numbers. Our code is freely available and can be readily adapted to any country or region.